Maths Syllabus for Class 11 (2016-17)
Three Hours Max. Marks -100
|I.||Sets and Functions||29|
|VI.||Statistics and Probability||12|
- Sets and their representations.
- Finite and Infinite sets.
- Empty set. Power set. Equal sets. Subsets.
- Properties of Complement Sets.
- Venn diagrams. Difference of sets.
- Complement of a set.
- Universal set. Subsets of a set of real numbers especially intervals (with notations).
- Union and Intersection of sets.
- Practical Problems based on sets.
- Ordered pairs, Cartesian product of sets.
- Cartesian product of the sets of real (upto R x R).
- Pictorial representation of a function, domain, co-domain and range of a function. Function as a special kind of relation from one set to another.
- Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Number of elements in the cartesian product of two finite sets.
- Sum, difference, product and quotients of functions.
- Real valued functions, domain and range of these functions: modulus, exponential, constant, polynomial,identity, rational, signum, logarithmic and greatest integer functions, with their graphs.
- Positive and negative angles.
- Definition of trigonometric functions with the help of unit circle.
- Truth of the sin2x+cos2x=1, for all x.
- Signs of trigonometric functions.
- Domain and range of trigonometric functions and their graphs.
- Measuring angles in radians and in degrees and conversion of one into other. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application.
- Deducing identities like the following: Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x.
- General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.
- Process of the proof by induction.
- Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers.
- The principle of mathematical induction and simple applications.
- Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations.
- Algebraic properties of complex numbers.
- Argand plane and polar representation of complex numbers.
- Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Square root of a complex number.
- Linear inequalities.
- Algebraic solutions of linear inequalities in one variable and their representation on the number line.
- Graphical solution of linear inequalities in two variables. Graphical solution of system of linear inequalities in two variables.
- Fundamental principle of counting.
- Factorial n. (n!)Permutations and combinations,
- Derivation of formulae and their connections, simple applications.
- History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle.
- General and middle term in binomial expansion, simple applications.
- Sequence and Series.
- Arithmetic Progression (A.P.). Arithmetic Mean (A.M.)
- Geometric Progression (G.P.), general term of a G.P.,
- Sum of n terms of a G.P., Arithmetic and Geometric series infinite G.P. and its sum, geometric mean (G.M.),
- Relation between A.M. and G.M.
- Formula for the following special sum
- Brief recall of two dimensional geometry from earlier classes. Shifting of origin.
- Slope of a line and angle between two lines.
- Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form.
- General equation of a line. Equation of family of lines passing through the point of intersection of two lines.
- Distance of a point from a line.
- Sections of a cone: circles, ellipse, parabola, hyperbola; a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section.
- Standard equations and simple properties of parabola, ellipse and hyperbola.
- Standard equation of a circle.
- Coordinate axes and coordinate planes in three dimensions.
- Coordinates of a point.
- Distance between two points and section formula.li>
- Derivative introduced as rate of change both as that of distance function and geometrically.
- Intuitive idea of limit.
- Limits of polynomials and rational functions, trigonometric, exponential and logarithmic functions.
- Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions.
- The derivative of polynomial and trigonometric functions.
- Mathematically acceptable statements.
- Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics.
- Validating the statements involving the connecting words difference between contradiction, converse and contrapositive.
- Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data.
- Analysis of frequency distributions with equal means but different variances.
- Random experiments; outcomes, sample spaces (set representation).
- Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with the theories of earlier classes.
- Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.